As curved moldings necessitate a stretching of the metal in order to accommodate them to both the curve of the elevation or plan and the curve of the profile at the same time, the patterns for their blanks can only be considered as flaring strips of metal in which the curve of the elevation or plan only is considered. The curve of the profile requires to be forced into them by machinery designed for that purpose, care being taken to make the width of the flaring strip sufficient to include the stretchout of the curve of the profile. Blanks for curved moldings thus become frustums of cones and are cut according to the principles of regular flaring articles, as explained in the preceding problems. The method of determining the exact flare necessary to produce a certain mold with the greatest facility is a matter to be determined by the nature of the profile and the kind of machinery to be used in forming the same. Usually a line is drawn through the extremities of the profile, as shown at A D in either of the two illustrations here given, Figs. 461 and 462, and is continued until it meets the center line, for length of radius, as shown at F.

Fig. 461. - Obtaining the Blank for a Curved Cove or Ovolo Molding'.

Fig. 462 - Obtaining the Blank for a Curved Ogee Molding.

Therefore, to describe the pattern of the blank from which to make a curved molding corresponding to the elevation A C E D, proceed in the same manner as though the side E C were to be straight. Through the center of the article draw the line B F indefinitely, and draw a line through the points C and E of one of the sides, which produce until it meets B F in the point F. Then F E will be the radius of the inside of the pattern. The radius of the outside is to be obtained by increasing F C an amount equal to the excess of the curved line E C over the straight line E C, as shown by the distance C S. Then F S is the radius of the outside of the pattern. The length of the pattern can be obtained as in previous problems.

PROBLEM 127. The Patterns for Simple Curved Moldings in a Window Cap.

In Fig. 468 is shown the elevation of a window cap, in the construction of which two curved moldings are required of the same profile, but curved in opposite directions. It is advisable to include as much in one piece as can be raised conveniently with the means at hand; therefore, the curved part of the profile with its fillets or straight parts adjacent and the two edges necessary for joining it to the face and roof pieces will be obtained in one piece. The method of developing the pattern for the blank is the same for both curves. The two pieces will raise to the form by the same dies or rolls, it being necessary only to reverse them in the machine. Before the blank for the middle piece can be developed it will be necessary to first construct a section upon the center line, as shown at S K; from all points in the mold and the center of the curve upon the center line project horizontal lines to the right. Draw-any vertical line, as H K, to represent the face of the cap in the section and at S draw the profile of the mold, as shown. The principle to be employed in striking the pattern is simply that which would be used in obtaining the envelope of the frustum of a cone of which A D is the axis.

Fig. 463.-Elevation of Window Cap.

Fig. 464 - Blank for Center Piece.

Fig. 465. -Blank for Side Piece.

The Patterns for Simple Curved Moldings in a Window Cap.

The general average of the profile is to be taken in establishing the taper of the cone, or, in other words, a line is passed through its extreme points. Draw a line through the profile in this manner and prolong it until it intersects A D in the point A, all as shown by C A. Then A is the apex of the cone, of which A C is the side and H D the top of the frustum. Divide the profile S, as in ordinary practice for stretchouts, into any number of spaces, all as shown by the small figures. Transfer the stretchout of the profile S on to the line A C, commencing at the point 1, as shown, letting the extra width extend in the direction of C. From any convenient center, as A in Fig. 464, with radius A C, describe the pattern, making the length of the arc equal to the length of the corresponding are in the elevation, all as shown by the spaces and numbers. From the same center draw arcs corresponding to points 9, 10 and 11 of the stretchout, thus completing this pattern.

For the pattern of the carved molding forming the end portion of the cup proceed in the same general manner. Upon any line drawn through the center N of the curve, as L M, construct a section of the mold, as shown at R. From N draw the perpendicular N B indefinitely. Through the average of the profile R, as before explained, draw the line to B, cutting N B in the point B, as shown. Lay off the stretchout of the profile upon this line, commencing at the point 1, in the same manner as explained in the previous operation. From any convenient point, as B1 in Fig. 465, as center, with radius B 1, describe the inner curve of the pattern, as shown, which in length make equal to the elevation, measuring upon the are 1, all as shown by the small figures, after which add the outer curves, as shown by E1 E2.

The straight portion forming the end of this molding, as shown in the elevation, is added by drawing, at right angles to the line E2 B1, a continuation of the lines of the molding of the required length, as shown in the pattern. Upon this end of the pattern a square miter is to be cut by the ordinary rule for such purposes, to join to the return at the end of the cap.

PROBLEM 128. The Pattern for the Curved Molding in an Elliptical Window Cap.

In Fig. 466 is shown the elevation and vertical section of a window cap elliptical in shape, the face of which is molded. In drawing the elevation such centers have been employed as will produce the nearest approach to a true ellipse after the manner described in Problem 76 of Geometrical Problems, page 65. The centers B, D and F, from which the respective segments of the elevation have been described, may then be used in obtaining patterns as follows: Through the center F, from which the arc forming the middle part of the cap is drawn, and at right angles to the center line of the cap G H, draw the line I K indefinitely. Project a section on the center line of the cap, as shown by P K at the right, the line P K being used as a common basis of measurement upon which to set off the semi-diameters of the various cones of which the blanks for the moldings form a Part. Through the average of the profile, as indicated, draw S R, producing the line until it meets I K. Divide the profile of the molding in the usual manner and lay off the stretchout, as indicated by the small figures. Then R S is the radius of the pattern of the middle segment of the cap.

With the dividers, measuring down from the profile, lay off on P K distances equal to the length of the radius A B, as shown by the point O, and of CD, as shown by the point M. Through these, points O and M, at right angles to P K, draw lines cutting S R in the points T and U. Then U S is the radius for the pattern of the segment C E of the elevation, and T S the radius of the pattern for the segment A C. In order to obtain the correct length of the pattern, not only as regards the whole piece, but also as regards the length of each arc constituting the curve, step off the length of the curved molding with the dividers upon any line of the elevation most convenient, as shown, numbering the spaces as indicated, and setting off a like number of spaces upon a corresponding line of the pattern. As a matter both of convenience and accuracy, the spaces used in measuring the ares are greater in the one of longest radius and are diminished in those of shorter radii, as will be noticed by examination of the diagram.

To lay off the pattern after the radii are obtained as above described, proceed as follows: Draw any straight line, as G1 H1 in Fig. 467, from any point in which, as F1, with radius equal to R S, as shown by F1 E1, describe an arc, as shown by E1 G1; and likewise, from the same center, describe other arcs cor-responding to other points in the stretchout of the pro-file. Make the length of the arc E1 G1 equal to the length of the corresponding arc in the elevation, as described above. From E1 to the center F1, by which this arc was struck, draw E1 F1. Set the dividers to the distance U S as radius, with which, measuring from E1 along the line E1 F1, establish D1 as center, from which describe arcs corresponding to the points in the profile, as shown from E1 to C1. Make E1 C1 equal to the length of the corresponding arc in the elevation, all as shown by the small figures. From C1 draw the line C1 D1 to the center by which this arc was struck.

Fig. 466. - Elevation and Section of Window Cap.

Fig. 467. - Blank for the Curved Molding.

Set the dividers to the distance T S in the section, and, measuring from C1 along the line C1 D1, establish the point B1, from which as a center strike arcs corresponding to those already described in the other section of the pattern. Make the length equal to the length of the corresponding segments in the elevation.

And draw the line A1 B1. Then A1 C1 E1 G1 is the half pattern corresponding to A C E G of the elevation.